set M = the carrier of L;
for u being set st u in the carrier of L holds
u in the carrier of L ;
then reconsider M = the carrier of L as Subset of L by TARSKI:def 3;
reconsider M = M as non empty Subset of L ;
take M ; :: thesis: M is add-closed
for x, y being Element of L st x in M & y in M holds
x + y in M ;
hence M is add-closed by Def1; :: thesis: verum